Reconstructing a matrix from a partial sampling of Pareto eigenvalues

Complementarity problems with respect to Loewnerian cones

“…The word "Success" in Table 1 means that the selected random initial point z 0 has led to a solution, i.e., to a root of (9). Of course, as in any Newton type method, one can perfectly well encounter a situation of failure (divergence or ill-conditioning).…”

“…Of course, one must accept the possibility of initializing the SNM with a large number of initial points. As shown in Table 4, the expected NIPs needed for detecting a solution grow rapidly with n. Table 3 SNM applied to (9) with κ = κ fb . The map L has the special form (17) We now turn the attention to the minimum complementarity function.…”

“…Besides, the system (21) is not square. By following a similar strategy as in [9,10], one may shift the attention to a certain "companion" system…”